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Noise resistance of RX coil is an equivalent resistance, which generates thermal noise.
Fig. 1 of attached image shows the equivalent circuit of RX coil for SPICE noise simulation. The noise resistance Rn
is formed by two frequency dependent resistances connected in series.
Resistance r1 is almost identical to the resistance of the RX coil, measured with a DC ohmmeter. However, the r1
grows with increasing frequency due to skin and proximity effect.
Resistance r2 due to energy dissipation in environment when soil under RX coil has lossy ferromagnetizm and / or
conductivity. It also increases with frequency. Noise resistance r2 is maximal when search head is immersed in sea
water and moves near to mineralized bottom.
Total noise resistance Rn =r1 + r2 is not important for a conventional metal detector because the gain of its RFA is
not limited by thermal noise at the imput, but by existing large AIR & GND signal and EMI (electromagnetic
interference). For example, the circuit diagram of RF amplifier in Fig. 2 is not properly designed for minimum thermal
noise, as was shown in another thread. Resistance of R1 should be less than the coil noise resistance Rn. We can
improve this using for example R1=82ohm, but in practice the SNR will not increase significant because 5534
opamp generates noise as a rn=1000 ohm resistor, ie much more than the Rn of coil and the 82 ohm resistor R1.
However at perfect designed sensing head and RFA circuit, the EMI and AIR & GND signals are suppressed in
input. In this case designer must ensure thermal noise at the input to be less than suppressed signals. Is needed an
amplifier build by only one PNP low noise transistor, as was shown in another thread. When the gain of RFA is
limited by thermal noise in input, the designer must calculate r1 for low noise but high for lightweight RX coil.
How designer must select the DC resistance of the RX coil? If he designed a RX coil having r1< r2 (searching at
worst environmental conditions), it has unnecessary increased the weight of the RX coil because is used more
metal without significant effect. The weight of the RX coil is important when to increase the SNR, the RX coil has
more turns. For this purpose, the calculation of L is made for a small resonance capacitance of tuned circuit, for
example 1nF as shown in Fig. 2.
To select DC resistance of RX coil, the designer needs to know the value of noise resistance r2 at worst condition.
The quiz question is:
How to measure the noise resistance Rn of RX coil?
HINT: If we connect the capacitor C1 in series to RX coil, the impedance of LC circuit in Fig. 1 is equal to Rn at
resonance frequency. To make measurement of Rn with a DC ohmmeter, we need a potentiometer to substitute LC
tank in measuring circuit.
Fig. 1 of attached image shows the equivalent circuit of RX coil for SPICE noise simulation. The noise resistance Rn
is formed by two frequency dependent resistances connected in series.
Resistance r1 is almost identical to the resistance of the RX coil, measured with a DC ohmmeter. However, the r1
grows with increasing frequency due to skin and proximity effect.
Resistance r2 due to energy dissipation in environment when soil under RX coil has lossy ferromagnetizm and / or
conductivity. It also increases with frequency. Noise resistance r2 is maximal when search head is immersed in sea
water and moves near to mineralized bottom.
Total noise resistance Rn =r1 + r2 is not important for a conventional metal detector because the gain of its RFA is
not limited by thermal noise at the imput, but by existing large AIR & GND signal and EMI (electromagnetic
interference). For example, the circuit diagram of RF amplifier in Fig. 2 is not properly designed for minimum thermal
noise, as was shown in another thread. Resistance of R1 should be less than the coil noise resistance Rn. We can
improve this using for example R1=82ohm, but in practice the SNR will not increase significant because 5534
opamp generates noise as a rn=1000 ohm resistor, ie much more than the Rn of coil and the 82 ohm resistor R1.
However at perfect designed sensing head and RFA circuit, the EMI and AIR & GND signals are suppressed in
input. In this case designer must ensure thermal noise at the input to be less than suppressed signals. Is needed an
amplifier build by only one PNP low noise transistor, as was shown in another thread. When the gain of RFA is
limited by thermal noise in input, the designer must calculate r1 for low noise but high for lightweight RX coil.
How designer must select the DC resistance of the RX coil? If he designed a RX coil having r1< r2 (searching at
worst environmental conditions), it has unnecessary increased the weight of the RX coil because is used more
metal without significant effect. The weight of the RX coil is important when to increase the SNR, the RX coil has
more turns. For this purpose, the calculation of L is made for a small resonance capacitance of tuned circuit, for
example 1nF as shown in Fig. 2.
To select DC resistance of RX coil, the designer needs to know the value of noise resistance r2 at worst condition.
The quiz question is:
How to measure the noise resistance Rn of RX coil?
HINT: If we connect the capacitor C1 in series to RX coil, the impedance of LC circuit in Fig. 1 is equal to Rn at
resonance frequency. To make measurement of Rn with a DC ohmmeter, we need a potentiometer to substitute LC
tank in measuring circuit.
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